Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Journal of Magnetic Resonance 212 (2011) 370–377

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Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band Joshua R. Biller a,b, Virginia Meyer a,b, Hanan Elajaili a,b, Gerald M. Rosen c,d,e, Joseph P.Y. Kao c,d,f, Sandra S. Eaton a,b,⇑, Gareth R. Eaton a,b a

Department of Chemistry and Biochemistry, University of Denver, Denver, CO 80208, United States Center for EPR Imaging in vivo Physiology, University of Denver, Denver, CO 80208, United States Center for EPR Imaging and In Vivo Physiology, University of Maryland, Baltimore, Baltimore, MD 21201, United States d Center for Biomedical Engineering and Technology, University of Maryland, Baltimore, Baltimore, MD 21201, United States e Department of Pharmaceutical Sciences, University of Maryland, Baltimore, Baltimore, MD 21201, United States f Department of Physiology, University of Maryland, Baltimore, Baltimore, MD 21201, United States b c

a r t i c l e

i n f o

Article history: Received 6 June 2011 Revised 21 July 2011 Available online 29 July 2011 Keywords: Spin–spin relaxation Spin–lattice relaxation Spin packet line width

a b s t r a c t Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T1T2 in the range of 0.50–1.1 ls at ambient temperature. Both spin–lattice relaxation T1 and spin–spin relaxation T2 are longer for 15N- than for 14N-nitroxides. The dominant contributions to T1 are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T1 on nitrogen nuclear spin state mI was observed for both 14N and 15N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Optimization of nitroxides as probes for in vivo EPR imaging requires understanding of multiple factors that contribute to improved signal-to-noise (S/N). The goal of the present study is to define for nitroxides (a) the features of the molecules that impact the inherent relaxation-determined spin packet line widths, (b) the relaxation mechanisms that dominate spin lattice relaxation, and (c) the structural features that determine the unresolved hyperfine splittings. These studies reveal patterns that guide the design and selection of nitroxides for imaging experiments. For low molecular weight nitroxides in water, EPR spectra at X-band and lower frequencies are near the rapid tumbling limit: tumbling correlation times (s) are of the order of 10 ps, T1T2, saturation recovery curves can be fit with a single exponential, and line widths and T2 are weakly dependent on frequency because the dominant anisotropic interaction is the frequency⇑ Corresponding author at: Department of Chemistry and Biochemistry, University of Denver, Denver, CO 80208, United States. Fax: +303 871 2254. E-mail address: [email protected] (S.S. Eaton). 1090-7807/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.jmr.2011.07.018

independent nuclear hyperfine. Recent work on the frequency dependence of T1 for nitroxides has focused on the slower tumbling regime with s values in the range of 109–1010 s [1–3] where T1 is dependent on frequency below X-band (9 GHz). However, in the fast tumbling regime T1 for nitroxides is predicted to be independent of frequency below X-band [4]. Thus, although the ultimate goal is imaging at frequencies in the 250 MHz to 1 GHz range, advantage was taken of the higher signal-to-noise (S/N) achievable with smaller sample size at X-band to explore concentration and structure dependence of relaxation times and line widths. The study included nitroxides with 6-member (1), unsaturated 5-member (2), or saturated 5-member (3) rings (Fig. 1). Each was studied with both 14N and 15N isotopes. Since substitution of 1H by 2H substantially narrows the EPR signal and improves S/N, the study focused on deuterium-substituted nitroxides. Nitroxide 2 was selected for study because the unique ring hydrogen has been shown to have a hyperfine splitting that is a convenient monitor of oxygen concentration [5]. The low concentration continuous wave (CW) line widths, spin-packet line widths required for simulations including all nuclear hyperfine splittings, and directly-measured relaxation T1 and T2 were compared.

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O

O D

D D D3C

H D CD3

N

D 3C

.

O

[1a] N = 14N [1b] N = 15N

CD3

D3C D3 C

R

NH2 CD3 N O

CD3

.

R3 C R3C

O

R

OH CR3

R N O

[2a] N = 14N [2b] N = 15N

.

CR3

[3a] R = H, N = 14N [3b] R = D, N = 15N

Fig. 1. Structures of nitroxides studied. The designations 1, 2, or 3 are used when referring to either nitrogen nuclear isotope. Tempone and mHCTPO are commonly used designations for 1 and 2, respectively.

2. Experimental 2.1. Preparation of nitroxides 1a and 1b with >98% isotope purity were purchased from CDN Isotopes (Quebec, Canada). A second sample of 1a was prepared as described in the following paragraphs. 2a and 2b were prepared as previously reported [5] and provided by Prof. Halpern (University of Chicago). The syntheses of 3a and 3b were reported previously [6]. 2.1.1. 4-Oxo-2,2,6,6-tetra(2H3)methyl-(3,3,5,5-2H4,1-14N)piperidine [4] This compound was prepared following the general procedure of Lin et al. [7] with minor modifications. In a dry box with a positive N2 flow, 14N2H4Cl (Cambridge Isotopes, 98% 3.45 g, 60 mmol) was added to a 250 mL round bottom flask, which contained oven-dried anhydrous Na2CO3 (3.18 g, 30 mmol) and oven-dried MgO (3.0 g, 75 mmol). After the addition was complete, acetoned6 (12.5 mL, 150 mmol; 99.9%) was introduced into the flask via a canula under N2 pressure. The flask was capped with a rubber septum, heated for 3 days in an oil bath at 50 °C, and then allowed to cool. Then, acetone-d6 (20 mL) was added to the flask and the resulting mixture was filtered. The filter cake was crushed into a fine powder, washed with dry ether and acetone-d6 (1:1 mixture, 20 mL) and again filtered; this procedure was repeated three more times. The combined filtrates were concentrated on a rotary evaporator to give a red liquid (6.0 g), a portion of which was distilled to yield a yellow liquid (bp 60–64 °C at 12 mm Hg) [7], which solidified upon cooling. Distillation of 4 did not significantly affect the yield of 1a; therefore, crude 4 was used for the next reaction without further purification. 2.1.2. 4-Oxo-2,2,6,6-tetra(2H3)methyl-1-(3,3,5,5-2H4,1-14N) piperidinyloxyl [1a] To a solution of crude 4-oxo-2,2,6,6-tetra(2H3)methyl(1,3,3,5,5-2H5,1-14N)piperidine [4] (6.0 g, 35.3 mmol) dissolved in D2O (60 mL), was added oven-dried Na4EDTA (0.55 g, 1.5 mmol) and oven-dried Na2WO4 (0.55 g, 1.7 mmol). Upon dissolution of the salts, H2O2 (30% in H2O, 6 mL) was added and the reaction was allowed to proceed in the dark for 8–10 days. The reaction mixture was filtered and extracted with ether (3  50 mL). The ether solution was first washed with cold dilute 2HCl (10% in D2O, 2  20 mL) and then a saturated solution of Na2CO3 in D2O (10 mL). The remaining ether solution was dried over anhydrous MgSO4, and then evaporated to dryness. This nitroxide was chromatographed using silica gel, eluting with hexane:ether (2:1) to afford 4-oxo-2,2,6,6-tetra(2H3)methyl-1-(3,3,5,5-2H4,1-14N)piperidinyloxyl 1a, as a red oil, which solidified in the cold (3.1 g,

48% yield). IR (CHCl3): 1720 cm1 (C = O). Anal. calculated for C92H1614NO2: C, 58.00; 2H, 8.65; 14N, 7.52. Found: C, 58.09; 2H, 8.77; 14N, 7.41. EPR spectra and relaxation times for this preparation of 1a and for the sample of 1a purchased from CDN isotopes were indistinguishable. 2.2. Preparation of solutions Weighed samples of radicals were dissolved in water. Solutions in thin-wall 0.97 mm i.d. Teflon tubing were placed inside 4 mm o.d. quartz tubes. Gaseous N2 was passed over the sample via a thin Teflon tube that extended to the bottom of the quartz sample tube. O2 and N2 exchange through the tubing. The purging was continued until no further change in line width or relaxation time was observed. Integrals of CW spectra were checked to ensure that water evaporation was small enough that it did not significantly change the solution concentrations. 2.3. Spectroscopy Experiments were performed at room temperature, which was ca. 20–22 °C at the sample position in the resonator. X-band CW EPR spectra were obtained on a Bruker EMX-Plus spectrometer. Microwave power incident on the sample, magnetic field modulation amplitude, and modulation frequency were adjusted to ensure that the observed line widths were not broadened by experimental parameters. Reproducibility of oxygen removal was checked. The effectiveness of the deoxygenation methodology was verified with an Oxylab pO2 fluorescent probe (Oxford Optronix, UK). Spectra of 1a, 2a, or 3b in D2O were essentially indistinguishable from those in H2O. The slightly higher viscosity of D2O than of H2O causes proportional increases in tumbling correlation times that could be detected by changes in T2 measured by spin echo. However, this change in T2 is within the uncertainty in determination of T2 by simulation of CW lineshapes. T2 relaxation times were measured by two-pulse electron spin echo on a Bruker E580 or on a locally-built pulsed spectrometer [8] with a Bruker ER4118-X5MS split ring resonator. Both spectrometers use nominal 1 kW TWT amplifiers. The time constant for spin echo dephasing is designated as Tm [9]. For a molecule tumbling rapidly in fluid solution Tm = T2 so in this paper the spin echo dephasing time constant is designated as T2. T1 relaxation times were measured by inversion recovery on these two spectrometers, or by saturation recovery on the E580 with a Bruker ER4118-X5MS split ring resonator or a home-built spectrometer [10] using the 5-loop-4-gap resonator described in Ref. [11]. Values of T1 obtained by inversion recovery and saturation recovery for selected samples were compared and found to be in good agreement, within experimental uncertainty. Inversion recovery inherently

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provides higher S/N, so that is the method of choice for T1 measurements of nitroxides in this fast motional regime. Values of T1 obtained by inversion recovery are reported in the tables. Results obtained on different spectrometers with several operators were in good agreement. 2.4. Fitting of exponentials to pulse data and simulations of CW spectra Two-pulse echo decays, inversion recovery curves, and saturation recovery curves fit well with a single exponential, using a least-squares criterion. Reported relaxation times are averages of at least three replicates. CW EPR spectra were simulated using the shareware EasySpin 3.1.6 (http://www.easyspin.org/) and using locally-written Fortran programs, with guidance from published hyperfine values for 1a [12], 2a [12,13], and saturated 5-member ring nitroxides (pyrrolidines) similar to 3a [14]. 2H couplings were calculated from literature values of 1H couplings using the ratio cD/cH = 0.153. Hyperfine couplings are sensitive to solvent [13], so small differences from previously reported values were allowed in the simulations. Spin packet line widths calculated from T2 were substituted into the Kivelson equation [15] for the dependence of line width on nuclear spin, DB ¼ A þ B mI þ C m2I [16]. Equations presented in Chasteen and Hanna were used to calculate the molecular tumbling correlation time s from the value of B [17]. Since 14N A = 16.1–16.4 G for 1, 2, and 3 in water at 20 °C, it was assumed that the anisotropic g and AN values also would be similar for the three nitroxides. Based on literature reports the following parameters were used in analyzing the tumbling correlation times: gx = 2.0092, gy = 2.0061, gz = 2.0022. Ax = 5.5, Ay = 6.3, and Az = 35.9 G for 14N [18,19]. Average values of s based on CW spectra for 14N and 15N analogs at three concentrations are 9, 13, and 19 ps for 1, 2, and 3, respectively. To fit these s values to the Stokes–Einstein equation (s = cslip V g/kT, V = molecular volume, k = Boltzmann’s constant) required cslip of 0.11, 0.15, and 0.21 for 1, 2, and 3, respectively. The value of cslip for 1 is similar to the previously reported values of 0.12 in 1:1 water glycerol [20] and 0.13 in glycerol [18]. Trends in the values of cslip are consistent with the expectation of increasing solute-solvent interaction for ketone < amide < acid. 3. Results 3.1. Spin–spin and spin–lattice relaxation times Directly-measured relaxation times for the six radicals in 0.25 mM aqueous solutions are summarized in Table 1 for the center-field lines of the 14N nitroxides and the low-field lines of the 15 N nitroxides. For the 14N-nitroxides T2 for the low-field line is 2–5% longer than for the center line and T2 for the high-field line Table 1 Relaxation times, spin packet widths and overall line widths in H2O at 0.25 mM.a Nitroxide

T1 (ls)b

T2 (ls)c

DBsp (G)d

DBpp (G)

1a 2a 3a 1b 2b 3b

0.59 0.67 0.72 0.81 0.86 1.0

0.56 0.53 0.57 0.64 0.60 0.75

0.12 0.12 0.11 0.10 0.11 0.087

0.16 0.51e 1.1 0.16 0.51 0.40

a Center-field line for 14N and low-field line for 15N in deoxygenated water at 20–22 °C. b Uncertainties are about ±0.03 ls. c Uncertainties are about ±0.02 ls. d Calculated from T2 using Eq. (1). e The partially-resolved doublet splitting is 0.51 G with DBpp for each component of 0.26 G.

Table 2 Average T1a (ls) at 0.030 mM in H2O and comparison with calculationsb. Nitroxide

Exp.a

Calc. with Eq. (2)

Calc. with Eqs. (2)–(4).

Calc. with Eqs. (2), (3), (5)c

1a 2a 3a 1b 2b 3b

0.75 0.84 0.87 0.91 1.0 1.05

1.3 1.9 2.7 1.3 1.9 2.7

0.72 0.80 0.91 0.81 0.94 1.1

0.75 0.83 0.94 0.84 0.97 1.1

a Experimental T1, average of values obtained for low-field, center-field, and high-field lines. b Calculations use s = 9, 13, and 19 ps for 1, 2, and 3, respectively. c b = 0.90.

is 25–60% shorter than for the center line. For the 15N-nitroxides T2 for the high-field lines is 25–60% shorter than for the low-field lines. The modest dependence of T2 on mI and similarity in values of T1 and T2 (Table 1) are consistent with the fast tumbling regime. For comparison with simulations of CW spectra, T2 was converted to peak-to-peak spin packet line widths, DBsp, using the relationship for a Lorentzian line,

2 6:56  108 Gs DBsp ðGÞ ¼ pffiffiffi ¼ T 2 ðsÞ 3cT 2

ð1Þ

The much larger overall line widths, DBpp, than spin packet line widths DBsp (Table 1) reflect the substantial contributions from hydrogen/deuterium hyperfine splittings. 3.2. Contributions to T1 Values of T1 in 0.25 mM aqueous solutions (Table 1) are in good agreement with a report at X-band for 0.5 mM solutions at 20 °C: T1 = 0.49 ls for 1a and T1 = 0.68 ls for 2a [2]. Although a dependence of T1 on mI was observed in the present study, recent models for nitroxide spin lattice relaxation do not include an mI dependence [3,4,9,16,20–22]. The contributions to T1 were therefore analyzed first for the average values observed for the 3 (or 2) values of mI as summarized in Table 2 for 0.030 mM solutions. The mI dependence is discussed separately in Section 3.2.2. At these low concentrations the Heisenberg exchange contributions to the measured T1 are negligible. Spin–lattice relaxation for nitroxides in fluid solution has been analyzed in terms of contributions from spin rotation (Eq. (2)), modulation of g and A anisotropy by molecular tumbling, and Generalized spin diffusion [3,4,9,16,20–22]. For nitroxides tumbling rapidly in deoxygenated fluid solution, spin rotation (Eq. (2)) makes a larger contribution to T1 than in slower tumbling regimes [4,20], but as shown in Table 2 spin rotation alone is not sufficient to fully account for the relaxation times. Generalized spin diffusion (GSD) includes contributions from methyl rotation and modulation of intermolecular and intramolecular dipolar spin–spin interaction [4]. Other than the impact of slowing tumbling due to increased viscosity, substitution of H2O by D2O did not change the relaxation times, which indicates that the intermolecular contribution to GSD is not significant for these experiments. With the exception of 3a and one hydrogen in 2, the nitroxides selected for study are perdeuterated, so intramolecular contributions from GSD are much smaller than for natural isotope abundance. Therefore GSD was not included in the calculations of T1. At X-band (and lower frequencies) the contribution from modulation of g anisotropy is more than an order of magnitude smaller than from modulation of A anisotropy [4,20,22] (Eq. (3)) so inclusion of g anisotropy with an expression analogous to Eq. (3) had negligible impact on calculated T1.

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1 T SR 1

P3 ¼

i¼1 ðg i

 g e Þ2

9s

ð2Þ

Table 3 Ratios of T1 for nitrogen hyperfine lines.a

where i = x, y, z and ge is 2.0023. 3.2.1. Modulation of anisotropic nuclear hyperfine by tumbling In recent papers the modulation of anisotropic nuclear hyperfine by tumbling has been described by Eq. (3), and called the END mechanism [4,22].

X 2 ¼ IðI þ 1Þ ðAi  AÞ2 JðxÞ T A1 9 i 1

ð3Þ

where Ai is a component of the nitrogen nuclear hyperfine in angular frequency units, A is the average nitrogen hyperfine, I is the nitrogen nuclear spin, and J(x) is the spectral density function. Experimental values of T1 (Tables 1 and 2) are systematically longer for nitroxides with 15N than with 14N, which is consistent with prior results [1,20,23]. The isotope effect arises from differences in both magnetic moment and nuclear spin I. 15N has a larger magnetic moment than 14N (l14N/l15N = 0.71) which increases Ai, but the I(I + 1) term offsets this difference, so the ratio of the 14N/15N coefficients in Eq. (3) is (0.71)2  I14N (I14N + 1)/I15N (I15N + 1) = 1.4. Thus, if modulation of anisotropic nitrogen hyperfine were the only contribution to T1, T1 for a 15N-containing nitroxide would be 1.4 times larger than for the analogous 14N-nitroxide. The T1(15N)/T1(14N) ratios in Table 2 are about 1.2, which is consistent with modulation of nitrogen hyperfine anisotropy, in addition to spin rotation that is independent of nitrogen hyperfine. When motion is isotropic, the Bloembergen Pound Purcell (BPP) spectral density function, Eq. (4) is frequently used [3,22].

J BPP ðxÞ ¼

s 1 þ ðxsÞ2

ð4Þ

Calculations of T1 using the experimentally determined values of the tumbling correlation time s and Eqs. (2)–(4) gave values in reasonable agreement with the experimental data (Table 2). However, prior work on nitroxide relaxation has raised questions about the suitability of the BPP spectral density function. In studies of the temperature dependence of line widths of peroxylamine disulfonate (Fremy’s salt) in glycerol:water mixtures [24], tumbling correlation times for 1a in deuterated solvents [18], and T1 for 1a in toluene-d8 [25] it was observed that the BPP spectral density function (Eq. (4)) did not adequately model the data and that better agreement could be obtained by adding a parameter e 4 as the coefficient of the (xs)2 term. The Cole–Davidson spectral density function (Eq. (5)) was developed in studies of dielectric relaxation [26] and has been applied to NMR as well as dielectric relaxation [27–29].

J CD ðxÞ ¼

1 sinðb  arctanðxsÞÞ

x

ð1 þ ðxsÞ2 Þb=2

ð5Þ

where b characterizes the distribution of correlation times. The smaller the value of b, the wider the distribution. For b = 1, JCD(x) reduces to JBPP(x). An EPR study of the temperature dependence of line widths for 1a in toluene at L-band to X-band used a Cole– Davidson spectral density function with b = 0.83 [30]. In a study of nitroxide T1 over a wide range of tumbling correlation times it was found that the Cole–Davidson spectral density function (Eq. (5)) provided a better fit with experimental data than did the BPP model. The values of b ranged from 0.37 in o-terphenyl to 0.67 in 1:1 water:glycerol [20]. Calculation of T1 including spin rotation (Eq. (2)) and modulation of hyperfine anisotropy using Eqs. (3) and (5) with b = 0.90 gave improved fit to the experimental data for 1, 2, and 3 (Table 2).

Nitroxide

CF T LF 1 =T 1

HF T CF 1 =T 1

HF T LF 1 =T 1

Replicates

1a 2a 3a 1b 2b 3b

1.11 ± 0.02 1.12 ± 0.03 1.16 ± 0.02

1.10 ± 0.04 1.08 ± 0.07 1.09 ± 0.04

1.22 ± 0.04 1.22 ± 0.07 1.26 ± 0.06 1.18 ± 0.03 1.19 ± 0.05 1.23 ± 0.02

33 10 12 12 11 10

a LF, CF, and HF designate the low-field, center-field, and high-field lines. For 14N mI = +1, 0, and 1 for the low-field, center-field, and high-field lines. For 15N mI = 0.5 and 0.5 for the low-field and high-field lines.

3.2.2. Dependence of T1 on nitrogen mI A dependence of T1 on nitrogen mI was observed (Table 3) with T1 decreasing in the order low field > center field > high field. Although the differences are small, they were reproducible and many replicate measurements gave values of the ratios that are significantly different from 1. In an early variable temperature study of nitroxides in sec-butyl-benzene a dependence of T1 on mI was observed, with magnitude comparable to experimental uncertainties [23]. A dependence of T1 on mI was not observed in more recent studies of nitroxides in viscous solutions [20,22], but differences of the order of 10% are comparable to estimated uncertainties. A combination of ELDOR and saturation data for 1a in toluene between 188 and 233 K (s = 11.8  1011–1.5  1011 s) found ratios of T1 for the low-field and high-field lines between about 1.1 and 1.25 (read from graph) [31], which indicates that the mI dependence of T1 (Table 3) persists at slower tumbling correlation times. Early models for nitroxide spin lattice relaxation [15,24,32,33] included terms with mI dependence as shown in the following equation.

  1 lB mI þ c2 ðDAÞ2 m2I JðxÞ m ¼ c 1 DA Dg  h T1

ð6Þ

where c1 = 0.4 or 0.65, c2 = 0.033 or 0.05, DA = Azz  0.5(Axx + Ayy) with A in angular frequency units, and Dg = gzz  0.5(gxx + gyy). We propose an empirical approach to modeling the mI dependence of T1. Since Eq. (3) for the END mechanism expresses the anisotropy differently than in Eq. (6) we propose the expression for the mI dependence shown in the following equation.

" # X 1 lB 0  ¼ c jðA  AÞðg  g Þj mI i i 1 h Tm 1 i

ð7Þ

The value of c01 that gives the best fit to the combined experimental data for 14N and 15N nitroxides (Table 4) is 0.32 ± 0.03. The good agreement between the values of c01 required to model the mI dependence of T1 for the 14N and 15N nitroxides confirms the linear

Table 4 Differences between relaxation ratesb for nitrogen hyperfine lines.a

a b c d

Nitroxide

HF c 1=T LF 1  1=T 1 experimental

HF d 1=T LF 1  1=T 1 Calc, Eq. (7)

1a 2a 3a 1b 2b 3b

0.32 ± 0.06 0.26 ± 0.08 0.29 ± 0.06 0.21 ± 0.03 0.19 ± 0.04 0.21 ± 0.01

0.26 0.30 0.30 0.18 0.21 0.22

Notation and number of replicates are the same as in Table 3. Units are 106 s1. Proportional to DmI = 2 for 14N, DmI = 1 for 15N. c01 ¼ 0:32.

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Table 5 Concentration dependence of spin packet line widths and widths in H2O at infinite dilution.

a b

Nitroxide

Intercept DBsp (G)a,b

Slope (mG/mM)a

1a 2a 3a 1b 2b 3b

0.09 0.09 0.09 0.07 0.07 0.07

100 160 80 120 170 80

Rounded to nearest 10 mG, which is the estimated uncertainty. Calculated from T2 measured by spin echo.

dependence of the mI term on nitrogen hyperfine anisotropy. For typical nitroxide g and A values, DA Dg is 1.5 times R(gi  g)(Ai  A) so c01 ¼ 0:32 makes the contribution from the mI dependent term in Eq. (7) smaller by a factor of 2–3 than that proposed in Eq. (6). Consistent with the predictions of Eq. (6), the experimental dependence of T1 on m2I is about an order of magnitude smaller than on mI, which is too small an effect, relative to experimental uncertainty, to accurately define. 3.2.3. Concentration dependence of T1 The concentration dependence of T1 (data not shown) is smaller than for T2 (Table 5), which is discussed in the following paragraph. It has been shown previously that in the concentration range 0.57– 53 mM T2 for Fremy’s salt was more dependent on concentration than was T1 (factor of 20 vs. factor of 3.4), and the concentration effect on T1 was attributed to Heisenberg exchange [34]. A spin lattice Heisenberg exchange relaxation process, which shortens T1, can occur when two colliding radicals have different ms. Since the populations of the two ms states are approximately equal, only half of the collisions involve radicals with different ms. The probability of Heisenberg exchange is smaller than the probability of colliding with a radical with different hyperfine interaction, which shortens T2. 3.3. Spin–spin relaxation The T2 of 0.53 ls for 2a (Table 1) is similar to values reported previously for aqueous solutions extrapolated to infinite dilution: 0.595 ls by electron spin echo at X-band and 0.47 ls by lineshape analysis at 250 MHz [35]. Near the rapid tumbling limit there are two contributions to T2 – incomplete motional averaging of g and hyperfine anisotropy and spin–lattice relaxation, T1. The similarity in T1 and T2 values in Table 1 indicates that T1 makes a major contribution to T2 and explains why T2 is systematically longer for the 15 N- than for the 14N-nitroxides. The concentration dependence of T2, was examined at four points between 0.02 and 0.30 mM, and the results are summarized in Table 5. The spin packet line widths extrapolated to infinite dilution are smaller (indicating longer T2) for the 15N-nitroxides than for the 14N-nitroxides. There is substantial variation in the concentration dependence of DBsp (Table 5). The concentration dependence for 2a, 160 ± 10 mG/mM, agrees within experimental uncertainty with previous reports of 167 ± 3 mG [36] or 144 mG/mM [16]. The 170 ± 10 mG/mM concentration dependence for 2b is similar to the previous report of 120 mG/mM [16]. The largest concentration dependence is observed for 2. The large doublet hydrogen/deuterium hyperfine splitting (Table 6) for 2 results in a higher probability of collision with a radical in a different nuclear spin state. The concentration dependence is smallest for 3, which is a carboxylic acid and is predominantly in its anionic form in neutral aqueous solution. The negative charge on 3 decreases the probability of col-

Table 6 Nitrogen and hydrogen/deuterium coupling constants (G) in H2O.a,b

N Methyl

Ring hydrogens

1a

2a

3a

3b

16.1 0.018 (12D)

16.1 0.027 (12D)

16.4 0.32 (3H) 0.28 (3H) 0.05 (3H) 0.04 (3H) 0.54 (1H) 0.14 (1 H) 0.12 (1H)

22.9 0.049 (3D)

0.0031 (4D)

0.51 G (1H)

0.043 (3D) 0.008 (3D) 0.006 (3D) 0.54 (1H)/0.083 (1D) 1:3 0.021 (1D) 0.018 (1D)

a Coupling constants for 1b and for 2b are the same as for the corresponding 14N analogs except for scaling of the nitrogen hyperfine coupling. b Hyperfine coupling constants are in good agreement with literature values for 1a [12], 2a [12,13], nitroxides similar to 3 [14].

lisions. The concentration dependence is slightly greater for 15N than for 14N. The smaller number of nitrogen nuclear spin states increases the effective concentration in each line, but also decreases the probability of colliding with a radical in a different spin state. 3.4. CW lineshapes As shown in Table 1 DBpp is significantly larger than DBsp, and within the set of nitroxides there are much larger variations in DBpp than for DBsp. Since decreasing DBpp increases S/N, optimization of probes for in vivo imaging requires characterization of structural features that give rise to differences in hyperfine splittings. In addition, for EPR oximetry the parameter of interest is the change in DBsp due to collision with molecular O2. Thus it is important to confirm that simulations that include all hydrogen/ deuterium hyperfine couplings give spin packet line widths that agree with values obtained directly by electron spin echo (Table 1). CW spectra of the mI = 0 lines for 1a, 2a, 3a and the low-field line for 3b are shown in Fig. 2. For each of the ring structures the low-field and center-field lines of 14N- and low-field lines of 15Nspecies have very similar line widths. The low field line of 3b (Fig. 2D and F) is much sharper than the center field line of 3a (Fig. 2C and E) because of the replacement of hydrogen by deuterium. The spectra of 3 shown in Fig. 2E and F were obtained in toluene, because the lower viscosity resulted in better resolution of the hydrogen hyperfine splitting (Fig. 2E) than was obtained in water. For each of the simulations the DBsp used in the simulation is in good agreement with the value obtained by electron spin echo. The hyperfine couplings used in the simulations are shown in Table 6. For 1 and 2 simulation of the CW spectra for natural isotope abundance samples (spectra not shown) using values of the 2 H hyperfine couplings appropriately scaled to 1H also were in good agreement with experiment. A striking feature of the simulations, and a key factor in the small DBpp for 1, is the small coupling to the ring methyls. Substituents such as –NH2 or –OH (or derivatives of these) in the 4-position of a piperidine-1-oxyl, cause a conformation in which the bulky substituent is equatorial, and there is a large difference between the hyperfine couplings to two inequivalent sets of six hydrogens: equatorial (aH = 0.4–0.5 G) and axial (aH  0 G) methyl groups [14,37], with resulting DBpp > 1 G [38]. If conformational dynamics are fast enough, the couplings to the axial and equatorial methyls are averaged and the twelve methyl hydrogens are equivalent on the EPR timescale. This is the case in the hydrogen-con-

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(Fig. 2C), and then in water where the hyperfine splittings are not resolved (Fig. 2C). The overall lineshape is consistent with previously reported hyperfine splittings for this class of nitroxides [14], but uncertainties are greater than for 1 or 2. For 3 the asymmetric substitution of the ring and slow ring dynamics results in four inequivalent methyl groups with different hyperfine couplings, and a broad unresolved spectrum. When the hydrogen couplings were scaled to the values expected for deuterium the calculated lineshape was narrower than observed for 3b. Simulations (Fig. 2D) indicate the presence of about 25% H (instead of D) for the unique ring H/D with large hyperfine coupling. Mass spectroscopy had shown essentially complete deuteration in 3b [38]. However the EPR lineshapes are more sensitive than mass spectroscopy to incomplete deuteration at the unique site of the large hyperfine splitting. 3.5. Comparison with literature values for nitroxides

Fig. 2. CW lineshapes in the absence of oxygen for center-field lines of (A) 1a in water, (B) 2a in water, (C) 3a in water, (D) low-field line of 3b in water (E) centerfield line of 3a in toluene, and (F) low-field line of 3b in toluene. For each of the plots the x axis spans 4 G and the y axis scale is arbitrary. Simulations (red lines) using the hydrogen/deuterium hyperfine couplings listed in Table 6 and the spin packet widths listed in Table 1 overlay the experimental spectra. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

taining analog of 1 (average aH = 0.11 G) [39] and in 2,2,6,6-tetramethyl-1-piperidinyloxyl (average aH = 0.22 G). A double bond or two hydrogens at the 4-position appears to be required for the conformational averaging to be fast enough on the EPR timescale to give small averaged couplings to the methyls [38]. In 3-carbamoyl-2,2,5,5-tetramethyl-3-pyrrolin-1-yloxyl, CTPO, 5, there are four inequivalent sets of three hydrogens, with almost equal couplings of about 0.2 G [5]. For 5 with normal isotope abundance there is resolved hyperfine coupling to the methyl hydrogens and to the ring hydrogen [5]. The resolution of the hydrogen hyperfine splittings is sensitive to the O2 concentration in solution. Complete deuteration of 5 results in hyperfine couplings that are too small to be resolved. The envelope of the unresolved deuterium couplings is a line that is broader than the resolved hydrogen hyperfine lines of 5, and is less responsive to O2 collisions. Deuteration of only the methyl groups of 5 produces 2 in which there is resolved splitting by the single ring hydrogen. Simulations were performed initially of the spectra of 3a in toluene, where there is partial resolution of the larger splittings

A summary of relaxation times for Fremy’s salt reported T1 = ca. 0.35 ls and T2 = ca. 0.25 ls in air-saturated aqueous solutions at room temperature [37] and T2 = 0.41 ls in degassed water [40]. Values of T1 at X-band for low-molecular weight nitroxides in low viscosity solvents near 20 °C [9] include 1a in sec-butyl-benzene, 0.47 ls [23]; tempol in sec-butyl-benzene, 0.41 ls [23]; 1a in toluene-d8, 0.45 ls [25]; 1a in water, 0.30 ls [41] and perdeuterated 15N-tempol in water, 1 ls (read from Fig 3 in [22]). The Freed group has performed extensive studies of the impact of molecular motion on lineshapes and T2 [42,43]. These values are in the range of about 0.5–1 ls, consistent with the results reported here. The spectrum of Fremy’s salt does not have unresolved hyperfine coupling. The line width extrapolated to low concentration was 0.097 [44], which is similar to the 0.09 G values reported for nitroxides in Table 5. The Fremy’s salt line width increases with concentration with a slope of 46 mG/mM between 1 and 40 mM in aqueous 0.05 M K2CO3 (read from Fig. 3 of Ref. [44]). The smaller concentration dependence of relaxation-determined line widths for Fremy’s salt relative to neutral nitroxides such as 1 and 2 in water (Table 5) probably is due to the negative charges on the anion, analogous to observations on collision broadening of nitroxides by paramagnetic transition metal complexes [45,46]. The concentration dependence of T2 and line width is expected to depend on charge surrounding the radical, spin distribution, overall size, solvent viscosity and pH. The trityl radicals used for in vivo imaging are larger than nitroxides and negatively charged [47], which makes relaxation less dependent on concentration than for neutral nitroxides such as 1 and 2. 3.6. Predictions related to frequency dependence In vivo EPR imaging experiments are performed at frequencies between about 250 MHz and 1.0 GHz [48]. The contributions to line widths from unresolved proton hyperfine are independent of frequency. At X-band and lower frequencies the anisotropy in nitrogen nuclear hyperfine dominates the terms that are averaged by tumbling and this contribution is independent of frequency, so the contributions to T2 from incomplete motional averaging at 250 MHz to 1 GHz are predicted to be about the same as at X-band. At 250 MHz the values of T2 for the low-field and center-field lines of 1a obtained by rapid scan are 0.41 and 0.53 ls for 0.50 and 0.10 mM solutions, respectively [49]. These are similar to T2 at Xband for the center-field line of 1a of 0.59 and 0.68 ls for 0.25 mM and 0.030 mM solutions, respectively. In this rapid tumbling regime T1T2 so the experimental values of T2 provide a lower limit on T1 and requires that for 1a T1 at 250 MHz is P0.53 ls in 0.10 mM aqueous solution. Calculations of T1 at 250 MHz including

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contributions from spin rotation (Eq. (2)) and modulation of nitrogen nuclear hyperfine interaction described by Eq. (3) + (4), (3) + (5), or (3) + (5) + (7) predict T1 for 1a at 250 MHz of 0.66– 0.78 ls in dilute aqueous solution. For 2a and 3a the longer tumbling correlation times predict somewhat shorter values of T1 at 250 MHz and 1.0 GHz than at X-band but all of the models predict values of T1 P 0.5 ls at 250 MHz. For nitroxide parameters the dependence of T1 on mI (Eq. (7)) at 250 MHz is predicted to be smaller than that observed at X-band. Thus the results of the Xband relaxation time studies should also apply at lower frequencies. 4. Conclusions The spin packet line widths in water (Table 1) are similar for the three 15N-substituted radicals and somewhat narrower than for the 14N-substituted analogs, due primarily to longer T1 for 15N than for 14N. The negative charge on 3, or a narrow line, such as for 1, decreased the concentration dependence. The largest contribution to overall line width differences was from hydrogen (or deuterium) hyperfine splittings. As a result of the differences in hyperfine splittings, the CW peak-to-peak signal amplitude for 1a is about nine times greater than that for 5 and four times greater than for 2a. Replacement of 14N by 15N improves signal amplitude by an additional factor of 1.5 due to the smaller number of hyperfine lines. The spectra and relaxation times show that in aqueous solution at ambient temperature the six nitroxides studied are near the rapid tumbling limit and have T1T2. The dominant contributions to spin lattice relaxation are modulation of nitrogen hyperfine anisotropy and spin rotation. T1 is less concentration dependent than T2. Relaxation times and line widths for these nitroxides at 250 MHz in the rapid tumbling regime are predicted to be similar to values at X-band. Thus the results obtained at X-band provide the basis for selection and design of nitroxide probes for in vivo imaging at low frequencies. Acknowledgments This work was partially supported by NIH Grants EB002807 and EB000557 to GRE and SSE, and P41 EB002034 to GMR and GRE; H.J. Halpern, PI. Discussion with James S. Hyde about the relative line widths of 14N and 15N nitroxides stimulated some of the measurements reported here. Compounds 2a and 2b were provided by Howard J. Halpern, University of Chicago. Velavan Kathirvelu, DU, assisted with preliminary measurements. We thank a reviewer for bringing Ref. [31] to our attention. References [1] W. Froncisz, T.G. Camenisch, J.J. Ratke, J.R. Anderson, W.K. Subczynski, R.A. Strangeway, J.W. Sidabras, J.S. Hyde, Saturation recovery EPR and ELDOR at Wband for spin labels, J. Magn. Reson. 193 (2008) 297–304. [2] J.S. Hyde, J.-J. Yin, W.K. Subczynski, T.G. Camenisch, J.J. Ratke, W. Froncisz, Spin-labeled EPR T1 values using saturation recovery from 2 to 35 GHz, J. Phys. Chem. B 108 (2004) 9524–9529. [3] R. Owenius, G.E. Terry, M.J. Williams, S.S. Eaton, G.R. Eaton, Frequency dependence of electron spin relaxation of nitroxyl radicals in fluid solution, J. Phys. Chem. B 108 (2004) 9475–9481. [4] C. Mailer, R.D. Nielsen, B.H. Robinson, Explanation of spin–lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR, J. Phys. Chem. A 109 (2005) 4049–4061. [5] H.J. Halpern, M. Peric, T.D. Nguyen, D.P. Spencer, B.A. Teicher, Y.J. Lin, M.K. Bowman, Selective isotopic labeling of a nitroxide spin label to enhance sensitivity for T2 oxymetry, J. Magn. Reson. 90 (1990) 40–51. [6] S.R. Burks, J. Bakhshai, M.A. Makowsky, S. Muralidharan, P. Tsai, G.M. Rosen, J.P.Y. Kao, 2H,15N-Substituted nitroxides as sensitive probes for electron paramagnetic resonance imaging, J. Org. Chem. 75 (2010) 6463–6467. [7] Y.J. Lin, B.A. Teicher, H.J. Halpern, Synthesis of 4-protio-3-carbamoyl-2,2,5,5tetraperdeuteromethyl-3-pyrrolin-1-yloxy (mHCTPO): a selectively isotopically labeled compound for use in T2 spin label oxymetry, J. Labelled Compd. Radiopharm. 28 (1990) 621–631.

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